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Self-stabilization in distributed systems is a technique to guarantee convergence to a set of legitimate states without external intervention when a transient fault or bad initialization occurs. Recently, there has been a surge of efforts in designing techniques for automated synthesis of self-stabilizing algorithms that are correct by construction. Most of these techniques, however, are not parameterized, meaning that they can only synthesize a solution for a fixed and predetermined number of processes. In this paper, we report a breakthrough in parameterized synthesis of self-stabilizing algorithms in symmetric networks, including ring, line, mesh, and torus. First, we develop cutoffs that guarantee (1) closure in legitimate states, and (2) deadlock-freedom outside the legitimate states. We also develop a sufficient condition for convergence in self-stabilizing systems. Since some of our cutoffs grow with the size of the local state space of processes, scalability of the synthesis procedure is still a problem. We address this problem by introducing a novel SMT-based technique for counterexample-guided synthesis of self-stabilizing algorithms in symmetric networks. We have fully implemented our technique and successfully synthesized solutions to maximal matching, three coloring, and maximal independent set problems for ring and line topologies. [ABSTRACT FROM AUTHOR]

Population protocols (Angluin et al. in PODC, 2004) are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions satisfying a strong fairness constraint. A population protocol is well specified if for every initial configuration C of devices, and every computation starting at C, all devices eventually agree on a consensus value depending only on C. If a protocol is well specified, then it is said to compute the predicate that assigns to each initial configuration its consensus value. While the computational power of well-specified protocols has been extensively studied, the two basic verification problems remain open: Is a given protocol well specified? Does a given protocol compute a given predicate? We prove that both problems are decidable by reduction to the reachability problem of Petri nets. We also give a new proof of the fact that the predicates computed by well-defined protocols are those definable in Presburger arithmetic (Angluin et al. in PODC, 2006). [ABSTRACT FROM AUTHOR]

We present an additional feature to the Challenge Handshake Authentication Protocol. It makes the protocol resilient to offline brute-force/dictionary attacks. We base our contribution to the protocol on the concept of a rewrite complement for ground term rewrite systems (GTRSs). We also introduce and study the notion of a type-based complement which is a special case of a rewrite complement. We show the following decision results. Given GTRSs A, C, and a reduced GTRS B over some ranked alphabet Σ, one can decide whether C is a type-based complement of A for B. Given a GTRS A and a reduced GTRS B over some ranked alphabet Σ, one can decide whether there is a GTRS C such that C is a type-based complement of A for B. If the answer is yes, then we can construct such a GTRS C. [ABSTRACT FROM AUTHOR]

Systems of Data Management Timed Automata (SDMTAs) are networks of communicating timed automata with structures to store messages and functions to manipulate them. We prove the decidability of the reachability problem for a subclass of SDMTAs which assumes an unbounded knowledge, and we analyze the expressiveness of the model and the considered subclass. In particular, while SDMTAs can simulate a Turing machine, and hence the reachability problem is in general undecidable, the subclass for which reachability is decidable, when endowed with a concept of recognized language, accepts languages that are not regular. As an application, we model and analyze a variation of the Yahalom protocol. [ABSTRACT FROM AUTHOR]

We consider the optimal makespan C( P, m, i) of an arbitrary set P of independent jobs scheduled with i preemptions on a multiprocessor with m identical processors. We compare the ratio for such makespans for i and j preemptions, respectively, where i < j. This ratio depends on P, but we are interested in the P that maximizes this ratio, i.e. we calculate a formula for the worst case ratio G( m, i, j) defined as $${G(m,i,j)=\max \frac{C(P,m,i)}{C(P,m,j)},}$$ where the maximum is taken over all sets P of independent jobs. [ABSTRACT FROM AUTHOR]

Correctness of recent database replication protocols has been justified in a rather informal way focusing only in safety properties and without using any rigorous formalism. Since a database replication protocol must ensure some degree of replica consistency and that transactions follow a given isolation level, previous proofs only focused in these two issues. This paper proposes a formalization using the I/O automaton model, identifying several components in the distributed system that are involved in the replication support (replication protocol, group communication system, database replicas) and specifying clearly their actions in the global replicated system architecture. Then, a general certification-based replication protocol guaranteeing the snapshot isolation level is proven correct. To this end, different safety and liveness properties are identified, checked and proved. Our work shows that some details of the replication protocols that were ignored in previous correctness justifications are indeed needed in order to guarantee our proposed correctness criteria. [ABSTRACT FROM AUTHOR]